In modem wireless communication systems, the increasing demand for higher bit rates is not easily accommodated by the available RF spectrum. Thus, the successful designs of transmission systems may no longer be aimed at providing redundancy for the ‘worst case’ channels but instead must be able to track quality of the link and adjust the transmission rate accordingly. In cellular systems, the problem of approaching channel capacity is rendered even more complex by interference caused by users transmitting their signals simultaneously. The problem with interference is that, in general, it is very difficult to predict its level. Hence, even if the transmitter knows the channel state perfectly at the beginning of transmission and maximizes throughput by changing the code rate accordingly, an instant increase of the interference power may render the signal undecodable.
One of the ways of dealing with this issue is to use a hybrid Automatic Repeat reQuest (HARQ) approach. An information block is first appended with the cyclic redundancy check (CRC) code, which is used for error detection and then encoded using the forward error correction (FEC). Using this approach, it is possible to detect possible errors in a frame and request additional retransmissions to provide the receiver with enough extra information to successfully decode the frame. In principle, there are two types of HARQ algorithms. In Type-I hybrid ARQ, the received packet is discarded after a negative CRC check and the whole packet is retransmitted. In Type-II, the techniques of soft packet combining and incremental redundancy (IR) are employed, which use both the currently retransmitted packet and previously received ones. In order to ensure high spectral efficiency of packet transmissions, Type-II is usually preferred since, with this approach, shorter blocks with additional code bits are needed for reliable transmission of the data and channel is used in a better way than in Type-I.
One method for decoding FEC codes in Type-II HARQ IR systems uses the bit-wise maximum a-posteriori (MAP) optimal BCJR (Bahl-Cocke-Jelinek-Raviv) algorithm. The BCJR algorithm can be used to decode all codes that can be represented by a trellis, but it is mainly used in component decoders of turbo codes and widely implemented in many existing deep space and 3 G cellular telephony systems. The BCJR algorithm can also be used to decode convolutional codes.
The most typical approach to designing HARQ systems is to create a set of rate compatible (RC) codes, which allows to gradually decrease the coding rate in subsequent retransmissions. At each rate, the weight spectrum of the given code is optimized according to some criterion, usually related to the maximization of the minimum Hamming distance. In case of turbo codes, the criteria can be more complicated. The BCJR differs from the commonly used Viterbi algorithm since the BCJR does not necessary produce sequences which are valid codewords, while the Viterbi algorithm always converges to an actual codeword (although it is possible that it will be a wrong one).
Since using the BCJR algorithm may result in the decoder converging to the non-codeword solution, any criterion relying purely on Hamming weight may not necessarily be optimal. As a result, if the BCJR algorithm is used, some frames will be not be decoded correctly and will contain convergence errors. Such errors cause lowered reliability of the output, which can be directly coupled to higher incidence of errors.